Structural study of an amorphous Cu64Ti36 alloy produced by mechanical alloying using XRD, EXAFS and RMC simulations

Solid State Communications 150 (2010) 1674–1678

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Structural study of an amorphous Cu64 Ti36 alloy produced by mechanical alloying using XRD, EXAFS and RMC simulations K.D. Machado a,∗ , G.A. Maciel a , D.F. Sanchez a , J.C. de Lima b , P. Jóvári c a

Departamento de Física, Centro Politécnico, Universidade Federal do Paraná, 81531-990, Curitiba, Paraná, Brazil

b

Departamento de Física, Universidade Federal de Santa Catarina, Trindade, Cx. P. 476, 88040-900, Florianópolis, Santa Catarina, Brazil

c

Hungarian Academy of Sciences, Research Institute for Solid State Physics and Optics, P.O.B. 49, H-1525 Budapest, Hungary

article

info

Article history: Received 10 May 2010 Received in revised form 2 June 2010 Accepted 17 June 2010 by M. Grynberg Available online 25 June 2010 Keywords: A. Amorphous alloys C. EXAFS E. X-ray scattering E. Monte Carlo simulations

abstract The structure of an amorphous Cu64 Ti36 alloy produced by mechanical alloying was studied by X-ray diffraction (XRD) and extended X-ray absorption fine structure (EXAFS) spectroscopy techniques and modeled through reverse Monte Carlo simulations using the total structure factor S (K ) and the EXAFS χ (k) oscillations on Cu K edge as input data. From the simulations the partial pair distribution functions gij (r ) and the bond-angle distribution functions 2ij` (cos θ ) were determined and, from these functions, average coordination numbers and average interatomic distances for the first neighbors were calculated. We also obtained information about the three-dimensional structures present in the alloy. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction Investigations on the production of amorphous alloys formed by binary and multicomponent alloys and about their physicochemical properties, including mechanical, electrical, thermal and magnetic properties, are growing both in number and in relevance. In addition to their unique and sometimes novel properties, these alloys also offer an opportunity to develop models about the relation between the alloy microstructure and these properties. As an example, bulk metallic glasses (BMG) have improved hardness, stiffness and strength [1], which are supposed to be associated with structural evolution at the atomic level. Concerning applications, some amorphous alloys can be used as precursors for a number of efficient catalysts for technically and ecologically important reactions. Specifically, they were found to show outstanding properties in ammonia synthesis [2] and have been suggested to use in global carbon dioxide recycling [3]. Crystalline and amorphous Cu–Ti alloys are of great scientific and technological interest due to some remarkable properties. These alloys are susceptible to age-hardening, and can be used in fabricating high strength springs, electrical contacts, diaphragms, and in developing corrosion and wear resistant materials [4]. They

∗

Corresponding author. Tel.: +55 4133613468; fax: +55 4133613418. E-mail address: [email protected] (K.D. Machado).

0038-1098/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2010.06.027

can also be used as precursors to Cu–Ti–O nanotubes [5] and as possible substitutes for expensive and toxic age-hardenable Cu–Be alloys. Amorphous Cu-based alloys, including Cu–Ti alloys, are of interest to chemist and materials scientists since they could be used as precursors of efficient, stable, and selective catalysts for technically important processes, like dehydration, dehydrogenation, or isomerization of aliphatic organic compounds [6,7]. Several studies about Cu–Ti alloys were performed in order to investigate the processes occurring with them when they transform a precursor into a catalyst [8,9]. Thus, it is important to obtain the atomic structure of such alloys, since its knowledge can help the understanding of their physico-chemical properties. Recently we have studied the local atomic order of an amorphous Cu64 Ti36 alloy [10] (a-Cu64 Ti36 ) produced by mechanical alloying (MA) [11] technique using extended X-ray absorption fine structure spectroscopy (EXAFS) data obtained on Cu and Ti K edges. Although this method furnished some structural data, the partial pair distribution functions gij (r ) and the bond-angle distribution functions Θij` (cos θ ) cannot be determined directly using this approach. Due to the relevance of these alloys and also to the possible applications listed above, we think these functions should be obtained, since they completely describe the atomic order of the amorphous material. Thus, we made reverse Monte Carlo (RMC) simulations [12–15] using the experimental total structure factor S (K ) obtained from X-ray diffraction (XRD) measurements and the EXAFS χ (k) oscillations obtained on Cu K edge as input data. These simulations furnished the gij (r ) functions and also the bond-angle

K.D. Machado et al. / Solid State Communications 150 (2010) 1674–1678

distribution functions Θij` (cos θ ). Structural parameters obtained were compared to those found from EXAFS in Ref. [10] and also from a new EXAFS analysis using a modern software. Some differences in average coordination numbers and average interatomic distances were found, and some possible reasons for these differences are discussed in the text. 2. Calculation details: structure factors and RMC simulations According to Faber and Ziman [16], the total structure factor

S (K ) is obtained from the scattered intensity per atom Ia (K ) through

 Ia (K ) − h f 2 (K )i − h f (K )i2 S (K ) = , h f (K )i2 n X n X S (K ) = wij (K )Sij (K ), 

(1)

(2)

i =1 j =1

where K is the transferred momentum, h f 2 (K )i =

P 2 i ci fi (K ),  2 h f (K )i2 = c f ( K ) , f ( K ) is the atomic scattering factor and i i i i ci is the concentration of atoms of type i, Sij (K ) are the partial structure factors and the coefficients wij (K ) are given by P

ci cj fi (K )fj (K )

wij (K ) =

h f (K )i2

.

(3)

The partial distribution functions gij (r ) are related to Sij (K ) through [17]

Sij (K ) = 1 +

4π ρ0

∞

Z

K

r gij (r ) − 1 sin(Kr )dr ,





0

where ρ0 is the density of the alloy. From gij (r ) functions the average interatomic distances and average coordination numbers associated with a coordination shell located between r1 and r2 can be determined through

R r2 r

rgij (r )4π r 2 dr

r1

gij (r )4π r 2 dr

hrij i = R 1r2

(4)

and

Z

r2

hNij i =

cj ρ0 gij (r )4π r 2 dr

(5)

r1

where spherical symmetry is supposed, furnishing a volume element dV = 4π r 2 dr. The structure factors defined by Eq. (1) can be used in RMC simulations. The algorithm of the standard RMC method is described elsewhere [14,15] and its application to different materials is reported in the literature [18–21]. When using XRD data only, the idea is to minimize the function

ψ

2 XRD

=

 RMC 2 m X S (Ki ) − S (Ki ) i =1

2 δXRD

(6)

(7)

where 2 ψEXAFS =

 RMC 2 m X χ (ki ) − χ (ki ) i =1

2 δEXAFS

is the function to be minimized. In Eq. (8), χ (ki ) is the experimental EXAFS signal, χ RMC (k) is its estimate obtained using RMC simulations and δEXAFS is the parameter related to the experimental errors in the EXAFS signal. To perform the simulations we have considered the RMC program available on the Internet [14] and cubic cells with 16 000 atoms. The total structure factor S (K ) obtained from XRD measurements and the EXAFS χ (k) oscillations on Cu K edge were used as input data in the simulations. 3. Experimental procedures As described in Ref. [10], amorphous Cu64 Ti36 samples were produced by milling Cu (Vetec 99.5%, particle size <10 µm) and Ti (BDH, 99.5%, particle size <10 µm) powders with initial nominal compositions Cu60 Ti40 . The powders were sealed together with several steel balls under argon atmosphere, in a steel vial. The weight ratio of the ball to powder was 5:1. The vial was mounted in a Spex 8000 shaker mill and milled for 9 h. A forced ventilation system was used to keep the vial temperature close to room temperature. The composition of the as-milled powder was measured using the Energy Dispersive Spectroscopy (EDS) technique, giving the composition Cu64 Ti36 , and impurity traces were not observed. EXAFS measurements on Cu K and Ti K edges were taken at room temperature in the transmission mode at beam line D04B – XAFS1 of the Brazilian Synchrotron Light Laboratory – LNLS (Campinas, Brazil). Three ionization chambers were used as detectors. The a-Cu64 Ti36 samples were formed by placing the powder onto a porous membrane (Millipore, 0.2 µm pore size) in order to achieve optimal thickness (about 50 µm) and they were placed between the first and second chambers. The beam size at the sample was 3 × 1 mm. The energy and average current of the storage ring were 1.37 GeV and 120 mA, respectively. XRD measurements were carried out at the BW5 beamline [22] at HASYLAB. All data were collected at room temperature using a Si (111) monochromator and a Ge solid state detector. The energy of the incident beam was 121.3 keV (λ = 0.102 Å). The cross section of the beam was 1 × 4 mm2 (h × v ). A thin-walled (10 µm) quartz capillary with 2 mm diameter was filled with the powder sample. The energy and average current of the storage ring were 4.4 GeV and 110 mA, respectively. To check for possible instabilities of the beam and the detector electronics, scattered intensities were recorded in 10 subsequent scans. The raw intensities were corrected for deadtime, background, polarization, detector solid angle and Compton scattering as described in [22], and a representative measurement furnished the total structure factor shown in Fig. 1, indicating the high quality of the measurements. The total structure factor was computed from the normalized intensity Ia (K ) according to Faber and Ziman [16]. 4. Results and discussion

where S (K ) is the experimental total structure factor, S RMC (K ) is its estimate obtained by RMC simulations, δXRD is a parameter related to the convergence of the simulations and to the experimental errors and the sum is over m experimental points. In our case, we added EXAFS data to the simulations, and the function 2 2 ψ 2 = ψXRD + ψEXAFS

1675

(8)

The first parameter to be determined was the density ρ0 of a-Cu64 Ti36 . Since it is not easy to determine ρ0 experimentally, because the alloy is a nanometric powder, we used a procedure similar to that described in Ref. [23] to obtain the density. We chose some values for the minimum distances between atoms and considering them and δ fixed, we made simulations for different values of the density of the particles in the simulation box. After reaching convergence, the parameter ψ 2 given by Eq. (7) will 2 fluctuate around an equilibrium value ψeq . Then, we chose the 2 density that furnished the smaller ψeq and used this value as our estimate for the density of the alloy. The minimum distances min between atoms were fixed in these simulations at rCu–Cu = 2.20 Å, min min rCu–Ti = 2.30 Å and rTi–Ti = 2.40 Å, and 16 000 atoms were used

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0

5

10

15

20

Fig. 1. XRD experimental (thin line) and RMC simulated (red squares) total structure factor for a-Cu64 Ti36 . Fig. 3. Partial distribution functions gijRMC (r ) obtained from the RMC simulations for a-Cu64 Ti36 .

2

0

-2

3

6

9

12

Fig. 2. Experimental (thin line) and RMC simulated (red squares) k3 -weighted EXAFS χ(k) signal at Cu K edge for a-Cu64 Ti36 . 3

(10 240 Cu and 5760 Ti). Then, we found ρ0 = 0.05425 atm/Å , which was the density used in the RMC simulations discussed below. Fig. 1 shows the experimental XRD S (K ) of a-Cu64 Ti36 (thin line). It has a very well defined main halo around 3.0 Å−1 , a broad halo from 4.0 to 6.7 Å−1 formed by two peaks at 5.1 and 5.9 Å−1 and a fourth peak at 7.8 Å−1 , besides other minor peaks. It should be noted that residual crystalline peaks of Cu and Ti elements or Cu–Ti crystalline phases are not observed, indicating the good homogeneity of the amorphous phase. Besides the total structure factor S (K ), the k3 -weighted EXAFS χ(k) signal on Cu K edge was also used as input data in the RMC simulations. It is shown in Fig. 2. The EXAFS signal shows smooth oscillations characteristic of amorphous samples, in agreement with the XRD S (K ). It should be noted that this signal was obtained after Fourier transforming k3 χ (k) on Cu edge into rspace using a Hanning weighting function considering the range [3.25, 13.6] Å−1 and transforming back the first coordination shell to k-space, considering the range [1.30, 2.67] Å. To study the local atomic order of a-Cu64 Ti36 we made several RMC simulations considering S (K ) and χ (k) together. First we made hard sphere simulations without experimental data to avoid possible memory effects of the initial configurations in the results. These simulations were run until we got at least 3 × 106 accepted moves. Then, to obtain an initial convergence RMC simulations considering only S (K ) were performed. Next, we added the EXAFS χ (k) oscillations and run the simulations

using both experimental data. We made simulations considering several values of minimum distances, and the best simulations were obtained when the values given above were used. Distances shorter than those were tested but did not furnished smaller ψ 2 values. The S RMC (K ) obtained from the best simulation is shown in Fig. 1, and the corresponding k3 -weighted χ RMC (k) is seen in Fig. 2. There is a good agreement between S (K ) and its simulation, and also between χ (k) and its simulation, which allows us to calculate relevant structural parameters, such as average coordination numbers and average interatomic distances. In this 2 series of simulations, the equilibrium value ψeq divided by the total number of data points used was around 121, and corresponds 2 2 to ψeq ,XRD /nXRD ≈ 145 and ψeq,EXAFS /nEXAFS ≈ 62, where ni , i = XRD, EXAFS, is the number of experimental data points obtained from the experimental technique i. The statistically independent configurations were collected considering at least 2 × 105 accepted movements between one configuration and the next. At the end of the simulations, about 24% of the generated movements were accepted. Fig. 3 shows the partial distribution functions gijRMC (r ) obtained from the simulations for a-Cu64 Ti36 . Some relevant points about the gijRMC (r ) functions have to be discussed. The first peak of RMC gCu–Cu (r ) is located between 2.10 and 3.20 Å and its maximum Cu–Cu occur at rmax = 2.60 Å. The corresponding average interatomic distance is given by hr Cu–Cu i = 2.69 Å (see Eq. (4)), and the average coordination number is hN Cu–Cu i = 7.8 (see Eq. (5)). All structural data obtained are given in Table 1. RMC (r ) function, its first peak, located Considering now the gCu–Ti between 2.20 and 3.30 Å, is formed by two overlapping peaks, Cu–Cu whose maxima are found at r1Cu–Ti ,max = 2.50 Å and r2,max = 2.90 Å, respectively. The average coordination numbers associated to these peaks are hN1Cu–Ti i = 1.2 and hN2Cu–Ti i = 1.3, and the average interatomic distances are hr1Cu–Ti i = 2.51 Å and hr2Cu–Ti i = 2.93 Å. Thus, the first Cu–Ti shell is located at hr Cu–Ti i = 2.72 Å, and the corresponding average coordination number is hN Cu–Ti i = 2.5. It is interesting to note that in the crystalline Cu2Ti phase (c-CuT i) Cu–Ti subshells are also found, and they are located at 2.58, 2.61 Cu–Ti and 2.63 Å, corresponding to a total of NCu = 5 neighbors. 2 Ti RMC Turning our attention to the gTi–Ti (r ) function, there are two well defined peaks between 2.40 and 3.50 Å, with maxima at Ti–Ti r1Ti–Ti ,max = 2.70 Å and r2,max = 3.20 Å, respectively. The first of these two peaks is the first Ti–Ti shell and corresponds to an average coordination number hN1Ti–Ti i = 2.8 located at hr1Ti–Ti i = 2.70 Å.

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Table 1 Structural data determined for a-Cu64 Ti36 from the RMC simulations using XRD and EXAFS data. The numbers in parentheses are the errors in the values. RMC: XRD + EXAFS Bond type hN i hr i (Å)

Cu–Tia

Cu–Cu 7.8 (0.5) 2.69 (0.08)

1.2 (0.3) 2.51 (0.07)

Ti–Ti 1.3 (0.3) 2.93 (0.08)

2.8 (0.4) 2.70 (0.07)

1.2 (0.4) 3.24 (0.06)

EXAFS analysis of Ref. [10] Cu–Cub

Bond type

hN i hr i (Å) 2 σ 2 (Å )

2.5 (0.4) 2.31 (0.02)

7.0 (1.0) 2.80 (0.01)

Cu–Ti 4.4 (0.6) 2.42 (0.02)

Ti–Ti 2.8 (0.4) 2.70 (0.01)

0.009 (0.001)

0.025 (0.002)

0.035 (0.004)

0.010 (0.001)

EXAFS analysis using IFEFFIT Bond type hN i hr i (Å) 2

σ 2 (Å ) a b

Cu–Cu 7.3 (0.9) 2.45 (0.01)

Cu–Ti 2.1 (1.5) 2.57 (0.05)

Ti–Ti 2.0 (0.6) 2.83 (0.07)

0.014 (0.001)

0.014 (0.004)

0.02 (0.01)

There are 2.5 ± 0.6 pairs at hr Cu–Ti i = 2.72 ± 0.06 Å. There are 9.5 ± 1.4 pairs at hr Cu–Cu i = 2.67 ± 0.02 Å.

Considering the second peak, its average coordination number is hN2Ti–Ti i = 1.2 and its average interatomic distance is hr2Ti–Ti i = 3.24 Å. It should be noted that in c-Cu2 Ti there are also two shells, Ti–Ti located at 2.93 and 3.32 Å, and each one furnishes NCu = 2 pairs. 2 Ti It is interesting to compare the results obtained here with those found in Ref. [10], and given in Table 1. Starting with Ti–Ti pairs, the values obtained here and in Ref. [10] are the same. Concerning Cu–Cu Cu–Cu pairs, in Ref. [10] we found hNEXAFS i = 9.5 ± 1.4 located at Cu–Cu hrEXAFS i = 2.67 ± 0.02 Å. Considering the error bars, the distances obtained are very similar. The difference in average coordination numbers is somewhat larger, but still within the error bars. The point to note was the use of two Cu–Cu subshells on EXAFS analysis in Ref. [10]. Considering now results for Cu–Ti pairs, the differences between data obtained from simulations and from EXAFS are more relevant, even considering the error bars. A possible reason for that is the quality of EXAFS data on Ti K edge, which is not as high as it is on Cu K edge (see Figs. 1 and 2 of Ref. [10]). In addition, the software WinXas97 [24] used to analyze the EXAFS data on Cu and Ti K edges in Ref. [10] could not handle both edges at the same time, as ARTEMIS [25] (from the IFEFFIT package) does now. This introduced a difficulty in the data analysis, since we had to obtain data on one edge and use some of them (hNij i, σij and hrij i, with i 6= j) on the other edge, obtaining new refined data that were used again on the first edge and so on, until reaching convergence on both edges. As the number of free parameters to use in these fits is limited and must obey the Nyquist criterion [26], we did not use two subshells for each pair i–j since the number of parameters would be larger than the maximum value allowed and we could not justify such choice at that time. In fact, it is important to keep the number of free parameters as small as possible. Thus, the procedure used could be responsible for the differences found in structural values associated with Cu–Ti pairs. To investigate this point, we made a new EXAFS analysis using IFEFFIT. Results obtained are also found in Table 1, and Fig. 4 shows the fits obtained. The agreement on Cu K edge is very good, but on Ti K edge is just reasonable. In addition, the values obtained for average coordination numbers agree within error bars with those obtained from the simulations, but average interatomic distances are different. First we tested the use of two Cu–Ti subshells, but the number of fitting parameters was too large and we could not get reliable fits. Then, we used only one Cu–Ti shell, and the fitting procedure became more stable. We think the overlap of the two Cu–Ti subshells as indicated by RMC simulations and the quality of EXAFS data on Ti K edge are complicating the EXAFS

Fig. 4. Fourier-filtered first shells (black lines) and their fits (red squares) for a-Cu64 Ti36 on Cu K edge (top) and on Ti K edge (bottom).

analysis and furnishing some spurious results. We believe the results obtained from the simulations are more reliable since we are using experimental data from two different techniques, XRD and EXAFS, and the three-dimensional structure obtained from the simulations must agree with both data and also with the other physical constraints, such as density and minimum approach distances. Besides gij (r ) functions, RMC simulations also furnish the bondangle distribution functions Θij` (cos θ ). These functions can be seen in Fig. 5. Since the vertical scale is the same, we can compare the six functions. All Θij` (cos θ ) functions indicate the presence of linear chains i–j–` (angles around 180°), but linear sequences i–Cu–j are more probable to be found than i–Ti–j (i, j = Cu, Ti) sequences. They also show halos centered around 57° and 109°, but relative intensities are different. Considering Cu–Cu–Cu sequences, angles around 57° are more probable to be found in the structure of the alloy than about 109° or 180°. A similar behavior is seen in ΘCu–Ti–Cu (cos θ ). ΘCu–Cu–Ti (cos θ ) and ΘTi–Ti–Cu (cos θ ) functions are similar to each other and both indicate a decrease in the relative quantity of sequences around 57° when compared to the other two sequences, which become more probable to be found. It is interesting to note that, at least in a-Cu64 Ti36 , the local atomic order is not as simple as the common models used to explain the structures of amorphous alloys, which consist of well separated shells, with average interatomic distances and average coordination numbers similar to the corresponding crystalline

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2.0

amorphous alloys, being also very different from its corresponding crystalline alloy.

1.5 1.0

Acknowledgements

0.5 0.0 2.0

We thank the Brazilian agency CNPq for financial support. This study was also partially supported by LNLS (proposal no XAS 799/01).

1.5 1.0 0.5

References

0.0 2.0 1.5 1.0 0.5 0.0 -1.0

-0.5

0.0

0.5

-1.0

-0.5

0.0

0.5

1.0

Fig. 5. Bond-angle distribution functions Θij` (cos θ) obtained from the RMC simulations for a-Cu64 Ti36 .

alloys. The local atomic order of a-Cu64 Ti36 is very different from that found in c-Cu2Ti considering average coordination numbers, average interatomic distances and distribution in coordination shells. We believe these features are associated to the preparation method, with introduces defects and stresses into the powders during the mill. 5. Conclusion The local atomic order of an amorphous Cu64 Ti36 alloy was investigated through RMC simulations using XRD S (K ) and EXAFS χ(k) data on Cu K edge. From the simulations, partial pair distribution functions gijRMC (r ) and bond-angle distribution functions Θij` (cos θ ) were obtained, and features of the first coordination shells were discussed. Average coordination numbers and average interatomic distances were determined and compared with results obtained by a previous EXAFS analysis [10]. The local atomic order of a-Cu64 Ti36 is not simple and somewhat different from the common models used to explain the structure of

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